Variance-Aware Multiple Importance Sampling

Equal-time comparison of bidirectional path tracing (BPT) with different MIS heuristics. The balance (b) and power (c) heuristics perform visibly worse
than using only the unidirectional path tracing samples that BPT includes (b). The error reduction in parentheses is w.r.t. the balance heuristic combination;
lower is better. Our variance-aware balance heuristic significantly improves the result (e), especially the direct illumination component (bottom row).

Abstract

Many existing Monte Carlo methods rely on multiple importance sampling
(MIS) to achieve robustness and versatility. Typically, the balance
or power heuristics are used, mostly thanks to the seemingly strong guarantees
on their variance. We show that these MIS heuristics are oblivious to
the effect of certain variance reduction techniques like stratification. This
shortcoming is particularly pronounced when unstratified and stratified
techniques are combined (e.g., in a bidirectional path tracer). We propose to
enhance the balance heuristic by injecting variance estimates of individual
techniques, to reduce the variance of the combined estimator in such
cases. Our method is simple to implement and introduces little overhead.

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Acknowledgments

We thank the anonymous reviewers for their valuable feedback.
The test scenes are slightly modified versions of those in the scene
repositories of PBRT and Benedikt Bitterli.
This work was supported by the Czech Science Foundation
Grant 19-07626S and Charles University Grant SVV-2017-260452.